The graph provided represents a quadratic function, which is a parabola opening downwards. We can determine the range of this function by analyzing the graph.

Key Observations:

• The vertex of the parabola is at the highest point, located at $(1, 5)$.
• Since the parabola opens downward, the range includes all $y$-values less than or equal to 5.

Range of the Function:

• The range is all $y$-values such that $y \leq 5$.
• In interval notation, the range is $(-\infty, 5]$.

Therefore, the correct answer choice should reflect that the range of the function $r$ is $(-\infty, 5]$.

Would you like further details, or do you have any questions?

Here are 5 related questions to further your understanding:

1. How do you determine the vertex of a quadratic function from its graph?
2. What does the range of a function represent?
3. How can you tell if a parabola opens upwards or downwards from the graph?
4. How would the graph and range change if the parabola opened upwards?
5. How do you calculate the domain of a quadratic function?

Tip: The range of a quadratic function depends heavily on whether the parabola opens upward or downward, and this is determined by the sign of the coefficient of $x^2$.